Cofiniteness

Cofiniteness

In mathematics, a cofinite subset of a set X is a subset A whose complement in X is a finite set. In other words, A contains all but finitely many elements of X. If the complement is not finite, but it is countable, then one says the set is cocountable.

These arise naturally when generalizing structures on finite sets to infinite sets, particularly on infinite products, as in the product topology or direct sum.

Read more about Cofiniteness:  Boolean Algebras, Cofinite Topology

Other articles related to "cofiniteness":

Cofiniteness - Other Examples - Direct Sum
... The analog (without requiring that cofinitely many are zero) is the direct product. ...